This review considers mechanisms by which transfer across the placenta takes place and how the capacity of the placenta to supply nutrients relates to fetal growth and vice versa. Blood flow through both uterine and umbilical circulations of the placenta, the structural properties of the placental exchange barrier and its related diffusional permeability, and the expression and activity of a wide range of transporter proteins in the syncytiotrophoblast, the transporting epithelium of the placenta, all need to be taken into account in considering placental supply capacity. We discuss the evidence that each of these factors affects, and is affected by, fetal growth rate and consider the regulatory mechanisms involved, with a particular focus on data that has emerged from study of the system A amino acid transporter. We consider that future work will build on the considerable foundation of knowledge regarding placental transfer mechanisms, as well as the other aspects of placental structure and function, to develop new diagnostic and therapeutic strategies for pregnancy complications, such as fetal growth restriction or overgrowth.